Advertisements
Advertisements
Question
Fill in the blanks:
y = ex .tan x
Differentiating w.r.t.x
`("d"y)/("d"x) = "d"/("d"x)("e"^x tan x)`
= `square "d"/("d"x) tanx + tan x "d"/("d"x) square`
= `square square + tan x square`
= `"e"^x [square + square]`
Solution
y = ex .tan x
Differentiating w.r.t.x
`("d"y)/("d"x) = "d"/("d"x)("e"^x tan x)`
= `"e"^x "d"/("d"x) tanx + tan x "d"/("d"x) "e"^x`
= `"e"^x sec^2x + tan x "e"^x`
= `"e"^x [sec^2x + tan x]`
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t.x. :
y = x5 tan x
Differentiate the following w.r.t.x. :
y = (x2 + 2)2 sin x
Differentiate the following w.r.t.x. :
y = `"e"^xsecx - x^(5/3) log x`
Differentiate the following w.r.t.x. :
y = `x^4 + x sqrt(x) cos x - x^2"e"^x`
Differentiate the following w.r.t.x. :
y = `sinx logx + "e"^x cos x - "e"^x sqrt(x)`
Differentiate the following w.r.t.x. :
y = `"e"^x tanx + cos x log x - sqrt(x) 5^x`
Differentiate the following w.r.t.x. :
y = `(x^2 sin x)/(x + cos x)`
Fill in the blanks:
y = `sinx/(x^2 + 2)`
Differentiating. w.r.t.x.
`("d"y)/("d"x) = (square "d"/("d"x) (sin x) - sin x "d"/("dx) square)/(x^2 + 2)^2`
= `(square square - sin x square)/(x^2 + 2)^2`
= `(square - square)/(x^2 + 2)^2`
Fill in the blanks:
y = (3x2 + 5) cos x
Differentiating w.r.t.x
`("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 5) cos x]`
= `(3x^2 + 5) "d"/("d"x) [square] + cos x "d"/("d"x) [square]`
= `(3x^2 + 5) [square] + cos x [square]`
∴ `(dx)/("d"y) = (3x^2 + 5) [square] + [square] cos x`
Fill in the blank:
Differentiate tan x and sec x w.r.t.x. using the formulae for differentiation of `"u"/"v" and 1/"v"` respectively
Select the correct answer from the given alternative:
If y = `(5sin x - 2)/(4sin x + 3)`, then `("d"y)/("d"x)` =
Select the correct answer from the given alternative:
Suppose f(x) is the derivative of g(x) and g(x) is the derivative of h(x).
If h(x) = a sin x + b cos x + c then f(x) + h(x) =
